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The amount of energy in a wave is related to its amplitude. Large-amplitude earthquakes produce large ground displacements and greater damage. As earthquake waves spread out, their amplitude decreases, so there is less damage the farther they get from the source.
- 16.2 Mathematics of Waves - University Physics Volume 1 - OpenStax
The amplitude, wave number, and angular frequency can be...
- 16.2 Mathematics of Waves - University Physics Volume 1 - OpenStax
Amplitude is something that relates to the maximum displacement of the waves. Furthermore, in this topic, you will learn about the amplitude, amplitude formula, formula’s derivation, and solved example.
The wave equation \(\frac{\partial^{2} y(x,t)}{\partial x^{2}} = \frac{1}{v^{2}} \frac{\partial^{2} y(x,t)}{\partial t^{2}}\) works for any wave of the form y(x, t) = f(x ∓ vt). In the previous section, we stated that a cosine function could also be used to model a simple harmonic mechanical wave.
The wave e can be described as having a vertical distance of 32 cm from a trough to a crest, a frequency of 2.4 Hz, and a horizontal distance of 48 cm from a crest to the nearest trough. Determine the amplitude, period, and wavelength and speed of such a wave.
The amplitude, wave number, and angular frequency can be read directly from the wave equation:
To find the amplitude, wavelength, period, and frequency of a sinusoidal wave, write down the wave function in the form y(x, t) = Asin(kx − ωt + φ). y (x, t) = A sin (k x − ω t + φ). The amplitude can be read straight from the equation and is equal to A.
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves).
